One of my many favorite problems to pose to my class is the Locker Problem. There are many versions of it on line, and you can also find some tech tools for use in the class. I pose the problem to my students and then give them a few minutes to accomplish steps one and two of the 4 step problem solving approach. After a little while we talk about what strategies the students have chosen. Draw a picture always comes up and through discussion we determine we don't want to draw 1000 lockers so we whittle it down to trying a simpler problem and looking for a pattern. After a little more time to work on the problem we talk about some other ways we can solve the problem and all of a sudden the students start getting creative! Some students use a deck of cards to represent lockers, some use puzzle pieces, some use pairs of scissors and some actually go to our 6th grade locker bay with colored post it notes. Eventually they begin to see a pattern emerge. I have the students present their work to the class and we review the pattern if necessary using the interactive hundreds chart on the Smartboard.
Here's the problem from CMP:
There are 1,000 lockers in the long hall of
Westfalls High. In preparation for the beginning of school, the janitor
cleans the lockers and paints fresh numbers on the locker doors. The
lockers are numbered from 1 to 1,000. When the 1,000 Westfalls High
students return from summer vacation, they decide to celebrate the
beginning of the school year by working off some energy.
- Student 1 opens every locker.
- Student 2 either opens or closes every other locker.
- Student 3 opens or closes every third locker. And so on, ...
